Theory of Radon Transform in the Concept of Computational (Numerical) Diameter and Methods of the Quasi-Monte Carlo Theory

Abstract

In the paper is shown that results of C(N)D-recovery of derivatives by the value at the point with using just only one relationships $\left\| f\right\| _{W_2^r (0,1)^s } \asymp \left\| Rf\right\| _{W_2^{r+\frac{s-1}{2} } (0,1)^s} $ implies Radon's scanning algorithm of an arbitrary open (not necessarily connected) bounded set, which is optimal among the all computational aggregates, constructed by arbitrary linear numerical information from the considered object with indicating the boundaries of the computational error, not affecting the final result.